Question

why is the anova table different in linear regression(1) vs the one used in Design of experiments(2) ? e.g. the column where degrees of freedom go, the degrees a freedom are accounted for in a different manner and wouldn't be the same in (1) vs (2).

Answer 1

Design of experiment consist of CRD, RBD, Factorial design, Split plot design etc.. So that contrains of each designs are different.. But in linear regression model there is only similar kinds of constrains .. That is why degree of freedom is different for both models...Mathematically there is no difference in Both models.. But in application level there is some difference..ANOVA (generally used in Design of experiments) is simply a special case of regression analysis where all of the predictor variables are categorical. ANOVA for regression consists of calculations that provide information about levels of variability within a regression model and form a basis for tests of significance